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Show that the angle between the diagonal...

Show that the angle between the diagonal of a cube is `cos^(-1)((1)/(3))`.

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Show that the tangent of an angle between the lines (x)/(a) + (y)/( b) = 1 and (x)/( a) - (y)/( b) = 1 is (2 ab)/( a^(2) - b^(2) ) .

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Knowledge Check

  • The angle between the two diagonals of a cube is .....

    A
    Parallel lines
    B
    Intersecting lines
    C
    Perpendicular lines
    D
    None of these

  • The angle between the two diagonals of a cube is .....

    A
    `cos^(-1)((sqrt(3))/(2))`
    B
    ` cos^(-1) ((1)/(sqrt2))`
    C
    `cos^(-1)(1/3)`
    D
    `cos^(-1)(1/(sqrt(6)))`

  • The edge of a cube is of length of a. The shortest distance between the diagonals of a cube an edge skew to it is ........

    A
    `a sqrt(2)`
    B
    `a`
    C
    `sqrt(2)/(a)`
    D
    `(a)/(sqrt(2))`

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